Electromagnetic Forming Analysis
Theory: from discharge current to magnetic pressure
Overview
How does electromagnetic forming apply force without touching the metal?
Releasing capacitor energy into a coil in an instant creates an extremely strong field for just tens of microseconds. A nearby metal workpiece carries opposing eddy currents that cancel the field change, and antiparallel currents repel, pushing the workpiece away from the coil. This force can be expressed as the pressure of the field trapped between coil and workpiece (magnetic pressure), proportional to field squared. Tens of MPa act in an instant, driving the workpiece above 100 m/s. Analysis first estimates current from the circuit equation, then field and pressure from current.
Discharge circuit and magnetic pressure
C is capacitance, V₀ charging voltage, L total circuit inductance (resistance neglected) and l single-turn coil length. Conditions: C = 200 μF, V₀ = 10 kV, L = 2 μH, l = 20 mm.
Skin depth, yield pressure and velocity bound
δ is aluminium's skin depth (resistivity 2.8×10⁻⁸ Ω·m), p_y static yield pressure of a tube of radius 25 mm and 1 mm wall, and v a velocity bound ignoring material strength.
A process born from strong-field research
Generating strong fields by capacitor discharge goes back to Kapitza's pulsed high-field research in the 1920s. In the 1950s and 60s methods using it to form metal were developed in the US and applied to tube joining and similar tasks. Recently it has regained attention for vehicle lightweighting, because high-speed forming improves the ductility of hard-to-form aluminium sheet and dissimilar metals can be joined without melting.
Worked examples
Example 1: discharge and magnetic pressure (200 μF, 10 kV, 2 μH)
| Item | Value |
|---|---|
| Stored energy | 10.0 kJ |
| Discharge frequency | 7.96 kHz |
| Time to peak | 31 μs |
| Peak current | 100 kA |
| Field in coil | 6.3 T |
| Magnetic pressure | 15.7 MPa |
| Aluminium skin depth | 0.94 mm |
| Charging voltage | Energy | Magnetic pressure |
|---|---|---|
| 5.0 kV | 2.5 kJ | 3.9 MPa |
| 7.5 kV | 5.6 kJ | 8.8 MPa |
| 10.0 kV | 10.0 kJ | 15.7 MPa |
Example 2: forming an aluminium tube (radius 25 mm, 1 mm wall)
| Material | Yield stress | Static yield pressure | Magnetic/yield pressure |
|---|---|---|---|
| Aluminium (annealed) | 55 MPa | 2.2 MPa | 7.1 |
| Aluminium (T6) | 275 MPa | 11.0 MPa | 1.4 |
Impulse over the first half-cycle is about 490 Pa·s, giving a velocity bound of about 180 m/s ignoring material strength.
Is there a problem if the skin depth, 0.94 mm, is about the tube thickness?
Magnetic pressure arises because the workpiece blocks the field, creating a field difference between its two sides. If skin depth is well below thickness, the field is almost fully blocked and pressure approaches B²/(2μ₀). If skin depth is comparable to thickness, some field passes through to the other side and the pressure difference shrinks, so real pressure is below this estimate. Remedies are raising discharge frequency (smaller inductance or capacitance) or adding a thin, highly conductive driver sheet to the workpiece. Once the workpiece moves, its gap to the coil widens, raising circuit inductance and lowering current. Capturing these effects needs coupled analysis solving circuit, electromagnetics and structure together.
Analysis workflow
- Estimate discharge current and frequency from the circuit equation and compare skin depth with thickness.
- Couple electromagnetics with the circuit to solve time-varying current and field.
- Pass Lorentz forces to structural analysis with large deformation and rate-dependent material.
- Feed workpiece motion back to the electromagnetic mesh to capture gap changes.
- Check coil strength and heating (the coil feels the same forces).
“The tube shrank less than calculated”
In compressing an aluminium tube, hand calculation of magnetic pressure predicted ample reduction, but actual reduction was about 60% of that. Coupled analysis showed a low discharge frequency, skin depth about equal to tube thickness, and field leaking inside the tube, reducing the pressure difference. As the tube started to shrink it moved away from the coil and current fell sooner. Lowering circuit inductance to raise frequency brought reduction to target.
Common mistakes
Mistakes and fixes
| Mistake | Effect | Fix |
|---|---|---|
| Ignoring skin depth | Pressure overestimated | Compare with thickness |
| Prescribed current | Current drop missed | Couple the circuit |
| Static material data | Wrong deformation | Rate dependence |
| Ignoring coil strength | Coil fails | Check coil stress |
| Ignoring workpiece heating | Properties change | Couple Joule heating |
I'd like to learn related topics.
Related pages include Lorentz force, MHD flow, magnetostriction, magnetic bearings and EMAT simulation.